range

Range

the positive difference between the largest and smallest values in a data set

Eg.

range of 4,8,5,6,9,1,3,5,8,6 is

1,3,4,5,5,6,6,8,8,9

9-1 = 8

mode

Mode

The most frequently occurring number in a
set of data

mode and most both have 4 letters

Eg.

mode of 3,5,7,7,9 is 7

mode of 2,2,4,6,6,8,11 is 2 and 6

Median

Median

The middle number in a set
of data after the data have been arranged in order

Eg.

median of 2,5,6,8,9 is 6

median of 1,3,6,8,9,10 is 7

Mean

Mean

A measure of central tendency

the sum of a set of values divided by the number of

values in the set

mean of 6,4,8 is

add up all the numbers and divide the results by how many numbers there are

6+4+8=18

18 divide it by 3 = 6

therefor the mean is 6

divisibility rules

1-all number
2-even numbers
3-sum is 3
4-divisible by 2 twice
5-end in 0 or 5
6-divisible by 2 or 3
8-divisible by 2 trice
9-end in 0

theoretical probability

Theoretical Probability- the expected probability of an event occurring.

BEDMAS

B=Brackets
E=Exponents
D=Division
M=Multiplication

A=Addition
S= Subtraction

divisibility rules

1-all number
2-even numbers
3-sum is 3
4-divisible by 2 twice
5-end in 0 or 5
6-divisible by 2 or 3
8-divisible by 2 trice
9-end in 0

integers

Negative integer are below 0 and positive integers are above 0.

eg

coordinate grid

every coordinate must go on a quadrant.
eg

lines

Lines

parallel lines-lines in the same plane that cross or intersect



intersecting-lines in the same plane that meet or cross

perpendicular-line in the same plane that intersect at 90 degree angle.

Range

the positive difference between the largest and smallest values in a data set

Eg.

range of 4,8,5,6,9,1,3,5,8,6 is

1,3,4,5,5,6,6,8,8,9

9-1 = 8

Mean

A measure of central tendency

the sum of a set of values divided by the number of

values in the set

mean of 6,4,8 is

add up all the numbers and divide the results by how many numbers there are

6+4+8=18

18 divide it by 3 = 6

therefor the mean is 6

Mode

The most frequently occurring number in a
set of data

mode and most both have 4 letters

Eg.

mode of 3,5,7,7,9 is 7

mode of 2,2,4,6,6,8,11 is 2 and 6

Median

The middle number in a set
of data after the data have been arranged in order

Eg.

median of 2,5,6,8,9 is 6

median of 1,3,6,8,9,10 is 7

Measures of Central Tendency

a value that represents the central of a data set

can be the mean,or mode

data set is a group of numbers that you MUST arrange in
order from least to greatest

Eg.

2,3,4,5,6,5,4,5,3,4,5,6,7,5,34,3

2,3,3,3,4,4,4,5,5,5,6,6,7,34

Circle Formulas

c= πd


c=2π r


d =2r


A=π R2 


Are is the measure of space  a two dimensional shape covers.

Quadrant

(+,+) quadrant I
(-,+) quadrant II
(-,-) quadrant III
(+,-) quadrant IV

2 types of Probabilty

Experimental probability- actually doing the trails.
Theoretical probability- what you expect to happen.
\

Mean,Median,Mode,Range,and Outlier

MEAN- add up all values divided by how many values there are.
MEDIAN- the middle number in a set of ordered values, might be the mean of 2 middle values.
MODE- the value that shows up the most.
RANGE- positive difference between largest and smallest value.
OUTLIER- values that are too big or too small compare to the other values.

Outlier

Outlier- a value that is much larger or smaller than the other data value
The data set may have more than 1 outlier or zero outliers
Outliers for - 1, 67, 66, 64, 65, 100 are 1 and 100

Range

The positive difference between the largest and smallest value in a data set
Range of - 4, 8, 5, 6, 9, 1, 3, 5, 8, 6 is
                 1, 3, 4, 5, 5, 6, 6, 8, 8, 9
9 - 1 = 8

Mean

Mean-a measure of central tendency
The sum of a set of values divided by the number of values in the set
mean of 6, 4, 8 is
Add up all the numbers and divide the result by how many number there are
6 + 4 + 8 = 18
18 ÷ 3 = 6
there for the mean is 6

Mode

The most frequently occurring number in a set of data
mode and most both have 4 letters
mode of 3, 5, 7, 7, 9, is 7
mode of 2, 2, 4, 6, 6, 8, 11 is 2 and 6
mode of 1, 2, 3, 5, is no mode
mode of 1 1, 1, 2, 2, 2, 3, 3, 3, is no mode
mode of 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, is 1, 2, and 3

Median

The middle number in a set of data after the data have been arrange in order
ex. median of 2, 5, 6, 8, 9, is 6
ex. median of 1, 3, 6, 8, 9, 10 is 7

Making A Angle Bisector

1. Compass point at the angle vertex make an arc through both arms

2. Compass point at vertex of 1st and arm makes another arc

3. Repeat step 2 from other arm

4. Draw line from arc intersecting to angle vertex

How To Make A Perpendicular Bisector

1. Open the compass to just over halfway of line segment
2. Sharp point at point A make an arc
3. Sharp point at point B make an arc
4. with ruler join the 2 intersections of the arc

Formulas for a Circle

Formulas for a Circle

There are 2 formulas to find the circumference of a circle. There is one formula to find the Area.
These are the formulas:
Circumference:
1.) C=πd (Circumference is equal to Pi times the diameter.)
2.) C=2πr (Circumference is equal to 2 times Pi times the radius.)

Integers

Integers

negative numbers represent values below zero and positive numbers represent values above zero.

eg. above and below sea level

EG. 1+(-2)=(-1) is an addition statement
3-(-1)=4 i an subtraction statement

M,M,M,R, and O

Mean,median,mode,range and outlier

Mean,median,mode,range and outlier
mean- add up all values divided b how many values there are
median- the middle number in a set of ordered values, might be the mean of 2 middle values.
range- positive difference between largest and smallest values
outlier- values that are too big or too small compared to the other values

Parallel Lines

Parallel Lines

-lines in the same place that never cross or intersect

Transformations

Transformations

Translation sliding along a strait line
Rotation-turn about a fixed point
Reflection-mirror image

Parallel Lines

-lines in the same place that never cross or intersect

Perpindicular Bisector

-a line that divides another line segment in a half and meets at a right angle
-equal line segment are shown with hash marks

Divisibility rules

0- ends in zero
1- all numbers
2- even numbers
3- sum of the digits is 3
4- divisible by 2 twice
5- ends in a 0m or 5
6- divisible by 2 and 3
8- divisible by 2 thrice
9- sum of the digits is 9
10 -ends in 0

Angle Bisector

Angle bisector
-a line that divides an angle into two equal parts
-equal angles are marked with the same symbol

factors 32
 1,2,4,8,16

Mean,median,mode,range and outlier

Mean,median,mode,range and outlier
mean- add up all values divided b how many values there are
median- the middle number in a set of ordered values, might be the mean of 2 middle values.
range- positive difference between largest and smallest values
outlier- values that are too big or too small compared to the other values

Intergers

Negative numbers represent values below zero and positive numbers represent values above zero

Integers

Integers

negative numbers represent values below zero and positive numbers represent values above zero.

eg. above and below he sea level

1+(-2)=(-1) is an addition statement
3-(-1)=4 i an subtraction statement

Measures of Central tendecy

Median-the middle number in a set of data after the data have been arranged in order
Mode-the most frequently occurring number in a set of data
Mean-a measure of central tendency
Range-the positive difference between the largest & smallest valves in a data set
Outlier- a value that is much larger or smaller than the other data value

Divisibility Rules

Divisibility Rules

0-end in zero
1- all numbers
2-even numbers
3- sum of the digit is 3
4- divisible by two twice
5- ends in a 0 or 5
6- divisible by 2 and 3
8- divisible by 2 thrice
9- sum of the digit is 9
10- ends in 0

transformations

translation-slide along a straight line
rotation-turn about a fixed point
reflection-mirror image

know how to do and describe each of them


know how to plot points
where does (1,-3) go on a coordinate line

Probability

Experiment probability - actually doing the trails
Theoretical probability - what you expect to happen
Probability - Likelihood or chance of an event occurring.
Outcomes - one possible result of a probability experiment.
Favorable outcome - a successful result in a probability experiment.

Transformations

Transformations
translation-slide along straight line
rotation- turn about a fixed point
reflection- mirror image

solve algebraic equation

a+5 = 7
a+5-5=7-5
a=2

b-6=3
b-6+6=3+6
b=9

2=s-5
2+5=5-5+5
7=S

Transformations

Translation - slide along a straight line
Rotation - turn about a fixed point
Reflection - mirror image

Coordinate Grid

(+,+) quadrant I
(-,+) quadrant II
(-,-) quadrant III
(+,-) quadrant IV

Area of a triangle

Picture explains it all.  the area of a triangle.

Variable is an unknown number.

An expression contains variables, operations, and numbers in any combination .

Convert Fractions to Percents

Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.

The simplest method is to use a calculator:

Steps: Divide the top of the fraction by the bottom, Then multiply the result by 100 and read off the answer !

Example: What is ⁵/₈ as a percent?

Get your calculator and type in "5 / 8 =", the calculator should show 0.625, then multiply by 100 and your answer is: 62.5% (remember to put the "%" so people know it is "per 100")

Of course you can do the division in your head or on paper if you don't have a calculator!

Another Method

Because percent means "per 100", you can try to convert the fraction to ^?/₁₀₀ form.

Follow these steps:

Step 1: Find a number you can multiply the bottom of the fraction by to get 100.

Step 2: Multiply both top and bottom of the fraction by that number.

Step 3. Then write down just the top number with the "%" sign.

Example 1: Express ³/₄ as a Percent

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25:

×25
3	=	75
4		100
×25

Step 3: Write down 75 with the percent sign:

Answer = 75%

Example 2: Express ³/₁₆ as a Percent

Step 1: We have to multiply 16 by 6.25 to become 100

Step 2: Multiply top and bottom by 6.25:

×6.25
3	=	18.75
16		100
×6.25

Step 3: Write down 18.75 with the percentage sign:

Answer = 18.75%

Convert Decimals to Fractions

(Multiply top and bottom by 10 until you get a whole number, then simplify)

To convert a Decimal to a Fraction follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction

Step 1: Write down 0.75 divided by 1:

0.75

1

Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):

× 100
0.75	=	75
1		100
× 100

(Do you see how it turns the top number 
into a whole number?)

Step 3: Simplify the fraction (this took me two steps):

	÷5		÷ 5
75	=	15	=	3
100		20		4
	÷5		÷ 5

Answer = ³/₄

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !

Adding Fractions with Unlike Denominators

Adding Fractions with Unlike Denominators:

Remember that given a fraction, such as , the top number is the numerator (namely 1) and the bottom number is the denominator (namely 2) 

Example 1:

Whenever you add fractions with unlike denominators, you need to make the denominators equal to each other by finding the least common denominator.  In this example, you need to multiply  by 5 to get .  Next, you need to multiply the second equation by 4 to get . Note that both fractions now have a common denominator.  Add in the same manner as with the unit Adding fractions with like denominators.

Example 2:

Whenever you add fractions with unlike denominators, you must make the denominators of the same value.  In this example, the easiest approach is to multiply 8 x 3 to get 24. Here, you multiply by 3 to get .  Then you multiply the second equation  by 8 to get .  Note that both addends have 24 as a denominator.  Add in the same manner as with the unit Adding fractions with like denominators.

Equivalent Fractions

Equivalent Fractions have the same value, even though they may look different.

These fractions are really the same:

1 2

=

2 4

=

4 8

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

The rule to remember is:

What you do to the top of the fraction
you must also do to the bottom of the fraction !

Mixed Fractions

(Also called "Mixed Numbers")

		A Mixed Fraction is a whole number and a proper fraction combined.  such as 1 3/4.
1 3/4
(one and three-quarters)

Examples

2 3/8

7 1/4

1 14/15

21 4/5